The generation of noncalssical states of light in integrated structures has attracted an evergrowing interest in recent years. A wide variety of optical states have been investigated, and some of the widespread sources include microring resonators, spiralled waveguides, and quantum dots. Recently, one of the emerging techniques adopted for the generation of such states relies on the interference of coherently pumped integrated sources. Although the interference between two microring resonators has already been demonstrated , as well as the interference between a particular configuration of sources , these phenomena are generally poorly investigated.
In this communication we advance these concepts and investigate the interference between four identical microring resonators, coherently pumped to produce photon pairs by degenerate spontaneous four-wave mixing (SFWM). This scheme cannot be considered a trivial generalization of the interference between two sources, for it gives us the opportunity to generate a wide variety of nonclassical states of light that are inaccessible with a combination of two-sources interferences. In particular, the state generated by our device is suitable for creating a GHZ (Greenberger-Horne-Zeilinger) state in which the information is encoded in the path degree of freedom. In our analysis we also establish direct correspondences between optical elements used for creating polarization-entangled GHZ states and integrated solutions used for creating path-encoded GHZ states.
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